To answer only one of the several questions (questions should only ask one question at a time):
If the crown is supreme (and can apparently be trusted to be impartial and exercise judicious restraint) in its judicial capacity while having the final say, then why not allow it simply in its prosecuting capacity to have absolute authority
The Canadian Charter of Rights and Freedoms, at s. 11(d) grants to any person charged with an offence, the right "to be presumed innocent until proven guilty according to law in a fair and public hearing by an independent and impartial tribunal."
The pre-conditions required for independence and impartiality are found in the judiciary, and not in the legislative or executive branches of government.
An essential component of the judicial independence guaranteed by s. 11(d) is "institutional independence." This requires "judicial control over the administrative decisions that bear directly and immediately on the exercise of the judicial function." See Valente v. The Queen,  2 S.C.R. 673, paras. 47, 52. The other two core components are security of tenure and financial independence.
Judicial independence has been defined as (ibid., para. 18):
the capacity of the courts to perform their constitutional function free from actual or apparent interference by, and to the extent that it is constitutionally possible, free from actual or apparent dependence upon, any persons or institutions, including, in particular, the executive arm of government, over which they do not exercise direct control.
Conversely, the members of the legislative and executive elements of the Crown do not benefit from the security of tenure, financial independence, and institutional independence that give the public the confidence in the impartiality of the judiciary.